



"""simple docstring"""





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def 						UpperCAmelCase  (		A						:    Union[str, Any]  ,					A						:    int=0.999  ,					A						:    List[str]="cosine"  ,					):

		'''simple docstring'''


		if alpha_transform_type == "cosine":

				def alpha_bar_fn(A						:    Tuple							):
						return math.cos((t + 0.008) / 1.008 * math.pi / 2							) ** 2

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(A						:    Union[str, Any]							):
						return math.exp(t * -12.0							)

		else:
				raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'							)

		_UpperCAmelCase							=		[]
		for i in range(A							):
				_UpperCAmelCase							=		i / num_diffusion_timesteps
				_UpperCAmelCase							=		(i + 1) / num_diffusion_timesteps
				betas.append(min(1 - alpha_bar_fn(A							) / alpha_bar_fn(A							)  ,					A							)							)
		return torch.tensor(A  ,					dtype=torch.floataa							)






class       lowercase__      (   _UpperCAmelCase,       _UpperCAmelCase     ):
							'''simple docstring'''







							_UpperCAmelCase   					=       [e.name for e in KarrasDiffusionSchedulers]
							_UpperCAmelCase   					=       2






							@register_to_config
							def __init__(	self						,							snake_case = 1000						,							snake_case = 0.00085						,							snake_case = 0.012						,							snake_case = "linear"						,							snake_case = None						,							snake_case = "epsilon"						,							snake_case = False						,							snake_case = False						,							snake_case = 1.0						,							snake_case = "linspace"						,							snake_case = 0						,							)      ->				Optional[Any]:


									if trained_betas is not None:
											_UpperCAmelCase							=		torch.tensor(lowerCAmelCase__						,							dtype=torch.floataa    )
									elif beta_schedule == "linear":
											_UpperCAmelCase							=		torch.linspace(lowerCAmelCase__						,							lowerCAmelCase__						,							lowerCAmelCase__						,							dtype=torch.floataa    )
									elif beta_schedule == "scaled_linear":
											# this schedule is very specific to the latent diffusion model.
											_UpperCAmelCase							=		(
											    torch.linspace(beta_start**0.5						,							beta_end**0.5						,							lowerCAmelCase__						,							dtype=torch.floataa    ) ** 2
											)
									elif beta_schedule == "squaredcos_cap_v2":
											# Glide cosine schedule
											_UpperCAmelCase							=		betas_for_alpha_bar(lowerCAmelCase__						,							alpha_transform_type='cosine'    )
									elif beta_schedule == "exp":
											_UpperCAmelCase							=		betas_for_alpha_bar(lowerCAmelCase__						,							alpha_transform_type='exp'    )
									else:
											raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'    )

									_UpperCAmelCase							=		1.0 - self.betas
									_UpperCAmelCase							=		torch.cumprod(self.alphas						,							dim=0    )

									#  set all values
									self.set_timesteps(lowerCAmelCase__						,							lowerCAmelCase__						,							lowerCAmelCase__    )
									_UpperCAmelCase							=		use_karras_sigmas






							def 							lowerCamelCase_ (	self						,							snake_case						,							snake_case=None    )      ->				List[str]:


									if schedule_timesteps is None:
											_UpperCAmelCase							=		self.timesteps

									_UpperCAmelCase							=		(schedule_timesteps == timestep).nonzero()

									# The sigma index that is taken for the **very** first `step`
									# is always the second index (or the last index if there is only 1)
									# This way we can ensure we don't accidentally skip a sigma in
									# case we start in the middle of the denoising schedule (e.g. for image-to-image)
									if len(self._index_counter    ) == 0:
											_UpperCAmelCase							=		1 if len(lowerCAmelCase__    ) > 1 else 0
									else:
											_UpperCAmelCase							=		timestep.cpu().item() if torch.is_tensor(lowerCAmelCase__    ) else timestep
											_UpperCAmelCase							=		self._index_counter[timestep_int]

									return indices[pos].item()






							@property
							def 							lowerCamelCase_ (	self    )      ->				List[Any]:


									if self.config.timestep_spacing in ["linspace", "trailing"]:
											return self.sigmas.max()

									return (self.sigmas.max() ** 2 + 1) ** 0.5






							def 							lowerCamelCase_ (	self						,							snake_case						,							snake_case						,							)      ->				torch.FloatTensor:
									_UpperCAmelCase							=		self.index_for_timestep(lowerCAmelCase__    )

									_UpperCAmelCase							=		self.sigmas[step_index]
									_UpperCAmelCase							=		sample / ((sigma**2 + 1) ** 0.5)
									return sample






							def 							lowerCamelCase_ (	self						,							snake_case						,							snake_case = None						,							snake_case = None						,							)      ->				List[Any]:
									_UpperCAmelCase							=		num_inference_steps

									_UpperCAmelCase							=		num_train_timesteps or self.config.num_train_timesteps

									# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
									if self.config.timestep_spacing == "linspace":
											_UpperCAmelCase							=		np.linspace(0						,							num_train_timesteps - 1						,							lowerCAmelCase__						,							dtype=lowerCAmelCase__    )[::-1].copy()
									elif self.config.timestep_spacing == "leading":
											_UpperCAmelCase							=		num_train_timesteps // self.num_inference_steps
											# creates integer timesteps by multiplying by ratio
											# casting to int to avoid issues when num_inference_step is power of 3
											_UpperCAmelCase							=		(np.arange(0						,							lowerCAmelCase__    ) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__    )
											timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
											_UpperCAmelCase							=		num_train_timesteps / self.num_inference_steps
											# creates integer timesteps by multiplying by ratio
											# casting to int to avoid issues when num_inference_step is power of 3
											_UpperCAmelCase							=		(np.arange(lowerCAmelCase__						,							0						,							-step_ratio    )).round().copy().astype(lowerCAmelCase__    )
											timesteps -= 1
									else:
											raise ValueError(
											    f'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'    )

									_UpperCAmelCase							=		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
									_UpperCAmelCase							=		np.log(lowerCAmelCase__    )
									_UpperCAmelCase							=		np.interp(lowerCAmelCase__						,							np.arange(0						,							len(lowerCAmelCase__    )    )						,							lowerCAmelCase__    )

									if self.config.use_karras_sigmas:
											_UpperCAmelCase							=		self._convert_to_karras(in_sigmas=lowerCAmelCase__						,							num_inference_steps=self.num_inference_steps    )
											_UpperCAmelCase							=		np.array([self._sigma_to_t(lowerCAmelCase__						,							lowerCAmelCase__    ) for sigma in sigmas]    )

									_UpperCAmelCase							=		np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )
									_UpperCAmelCase							=		torch.from_numpy(lowerCAmelCase__    ).to(device=lowerCAmelCase__    )
									_UpperCAmelCase							=		torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2    ), sigmas[-1:]]    )

									_UpperCAmelCase							=		torch.from_numpy(lowerCAmelCase__    )
									_UpperCAmelCase							=		torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2    )]    )

									if str(lowerCAmelCase__    ).startswith('mps'    ):
											# mps does not support float64
											_UpperCAmelCase							=		timesteps.to(lowerCAmelCase__						,							dtype=torch.floataa    )
									else:
											_UpperCAmelCase							=		timesteps.to(device=lowerCAmelCase__    )

									# empty dt and derivative
									_UpperCAmelCase							=		None
									_UpperCAmelCase							=		None

									# for exp beta schedules, such as the one for `pipeline_shap_e.py`
									# we need an index counter
									_UpperCAmelCase							=		defaultdict(lowerCAmelCase__    )






							def 							lowerCamelCase_ (	self						,							snake_case						,							snake_case    )      ->				List[str]:
									_UpperCAmelCase							=		np.log(lowerCAmelCase__    )

									# get distribution
									_UpperCAmelCase							=		log_sigma - log_sigmas[:, np.newaxis]

									# get sigmas range
									_UpperCAmelCase							=		np.cumsum((dists >= 0)						,							axis=0    ).argmax(axis=0    ).clip(max=log_sigmas.shape[0] - 2    )
									_UpperCAmelCase							=		low_idx + 1

									_UpperCAmelCase							=		log_sigmas[low_idx]
									_UpperCAmelCase							=		log_sigmas[high_idx]

									# interpolate sigmas
									_UpperCAmelCase							=		(low - log_sigma) / (low - high)
									_UpperCAmelCase							=		np.clip(lowerCAmelCase__						,							0						,							1    )

									# transform interpolation to time range
									_UpperCAmelCase							=		(1 - w) * low_idx + w * high_idx
									_UpperCAmelCase							=		t.reshape(sigma.shape    )
									return t






							def 							lowerCamelCase_ (	self						,							snake_case						,							snake_case    )      ->				torch.FloatTensor:
									_UpperCAmelCase							=		in_sigmas[-1].item()
									_UpperCAmelCase							=		in_sigmas[0].item()

									_UpperCAmelCase							=		7.0  # 7.0 is the value used in the paper
									_UpperCAmelCase							=		np.linspace(0						,							1						,							lowerCAmelCase__    )
									_UpperCAmelCase							=		sigma_min ** (1 / rho)
									_UpperCAmelCase							=		sigma_max ** (1 / rho)
									_UpperCAmelCase							=		(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
									return sigmas






							@property
							def 							lowerCamelCase_ (	self    )      ->				Dict:
									return self.dt is None






							def 							lowerCamelCase_ (	self						,							snake_case						,							snake_case						,							snake_case						,							snake_case = True						,							)      ->				Union[SchedulerOutput, Tuple]:
									_UpperCAmelCase							=		self.index_for_timestep(lowerCAmelCase__    )

									# advance index counter by 1
									_UpperCAmelCase							=		timestep.cpu().item() if torch.is_tensor(lowerCAmelCase__    ) else timestep
									self._index_counter[timestep_int] += 1

									if self.state_in_first_order:
											_UpperCAmelCase							=		self.sigmas[step_index]
											_UpperCAmelCase							=		self.sigmas[step_index + 1]
									else:
											# 2nd order / Heun's method
											_UpperCAmelCase							=		self.sigmas[step_index - 1]
											_UpperCAmelCase							=		self.sigmas[step_index]

									# currently only gamma=0 is supported. This usually works best anyways.
									# We can support gamma in the future but then need to scale the timestep before
									# passing it to the model which requires a change in API
									_UpperCAmelCase							=		0
									_UpperCAmelCase							=		sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

									# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
									if self.config.prediction_type == "epsilon":
											_UpperCAmelCase							=		sigma_hat if self.state_in_first_order else sigma_next
											_UpperCAmelCase							=		sample - sigma_input * model_output
									elif self.config.prediction_type == "v_prediction":
											_UpperCAmelCase							=		sigma_hat if self.state_in_first_order else sigma_next
											_UpperCAmelCase							=		model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
											    sample / (sigma_input**2 + 1)
											)
									elif self.config.prediction_type == "sample":
											_UpperCAmelCase							=		model_output
									else:
											raise ValueError(
											    f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'    )

									if self.config.clip_sample:
											_UpperCAmelCase							=		pred_original_sample.clamp(
											    -self.config.clip_sample_range						,							self.config.clip_sample_range    )

									if self.state_in_first_order:
											# 2. Convert to an ODE derivative for 1st order
											_UpperCAmelCase							=		(sample - pred_original_sample) / sigma_hat
											# 3. delta timestep
											_UpperCAmelCase							=		sigma_next - sigma_hat

											# store for 2nd order step
											_UpperCAmelCase							=		derivative
											_UpperCAmelCase							=		dt
											_UpperCAmelCase							=		sample
									else:
											# 2. 2nd order / Heun's method
											_UpperCAmelCase							=		(sample - pred_original_sample) / sigma_next
											_UpperCAmelCase							=		(self.prev_derivative + derivative) / 2

											# 3. take prev timestep & sample
											_UpperCAmelCase							=		self.dt
											_UpperCAmelCase							=		self.sample

											# free dt and derivative
											# Note, this puts the scheduler in "first order mode"
											_UpperCAmelCase							=		None
											_UpperCAmelCase							=		None
											_UpperCAmelCase							=		None

									_UpperCAmelCase							=		sample + derivative * dt

									if not return_dict:
											return (prev_sample,)

									return SchedulerOutput(prev_sample=lowerCAmelCase__    )






							def 							lowerCamelCase_ (	self						,							snake_case						,							snake_case						,							snake_case						,							)      ->				torch.FloatTensor:
									_UpperCAmelCase							=		self.sigmas.to(device=original_samples.device						,							dtype=original_samples.dtype    )
									if original_samples.device.type == "mps" and torch.is_floating_point(lowerCAmelCase__    ):
											# mps does not support float64
											_UpperCAmelCase							=		self.timesteps.to(original_samples.device						,							dtype=torch.floataa    )
											_UpperCAmelCase							=		timesteps.to(original_samples.device						,							dtype=torch.floataa    )
									else:
											_UpperCAmelCase							=		self.timesteps.to(original_samples.device    )
											_UpperCAmelCase							=		timesteps.to(original_samples.device    )

									_UpperCAmelCase							=		[self.index_for_timestep(lowerCAmelCase__						,							lowerCAmelCase__    ) for t in timesteps]

									_UpperCAmelCase							=		sigmas[step_indices].flatten()
									while len(sigma.shape    ) < len(original_samples.shape    ):
											_UpperCAmelCase							=		sigma.unsqueeze(-1    )

									_UpperCAmelCase							=		original_samples + noise * sigma
									return noisy_samples






							def __len__(	self    )      ->				Any:
									return self.config.num_train_timesteps



def 							UpperCAmelCase		(       lowercase				,     lowercase				):







				"""simple docstring"""



				__lowercase					     =				word.split()

				def justify(lowercase				,     lowercase				,     lowercase				) -> str:
								__lowercase					     =				max_width - width
								__lowercase					     =				len(lowercase				)
								if len(lowercase				) == 1:
												# if there is only word in line
												# just insert overall_spaces_count for the remainder of line
												return line[0] + " " * overall_spaces_count
								else:
												__lowercase					     =				words_count - 1
												# num_spaces_between_words_list[i] : tells you to insert
												# num_spaces_between_words_list[i] spaces
												# after word on line[i]
												__lowercase					     =				spaces_to_insert_between_words * [
												    overall_spaces_count // spaces_to_insert_between_words
												]
												__lowercase					     =				(
												    overall_spaces_count % spaces_to_insert_between_words
												)
												# distribute spaces via round robin to the left words
												for i in range(lowercase				):
																num_spaces_between_words_list[i] += 1
												__lowercase					     =				[]
												for i in range(lowercase				):
																# add the word
																aligned_words_list.append(line[i]				)
																# add the spaces to insert
																aligned_words_list.append(num_spaces_between_words_list[i] * ''' '''				)
												# just add the last word to the sentence
												aligned_words_list.append(line[-1]				)
												# join the aligned words list to form a justified line
												return "".join(lowercase				)

				__lowercase					     =				[]
				__lowercase					     =				[]
				__lowercase					     =				0
				for word in words:
								if width + len(lowercase				) + len(lowercase				) <= max_width:
												# keep adding words until we can fill out max_width
												# width = sum of length of all words (without overall_spaces_count)
												# len(word) = length of current word
												# len(line) = number of overall_spaces_count to insert between words
												line.append(lowercase				)
												width += len(lowercase				)
								else:
												# justify the line and add it to result
												answer.append(justify(lowercase				,     lowercase				,     lowercase				)				)
												# reset new line and new width
												__lowercase     ,	__lowercase					     =				[word], len(lowercase				)
				__lowercase					     =				max_width - width - len(lowercase				)
				answer.append(''' '''.join(lowercase				) + (remaining_spaces + 1) * ''' '''				)
				return answer


if __name__ == "__main__":
		from doctest import testmod

		testmod()